Finding Appropriate z*Values for Given Confidence Levels
The three practice questions here can help you achieve an understanding of the relationship between values of z and the confidence level needed for a margin of error. Use the following table to find the appropriate z*value for the confidence levels given except where noted.
Sample questions

The Ztable and the preceding table are related but not the same. To see the connection, find the z*value that you need for a 95% confidence interval by using the Ztable:
Answer: 1.96
First off, if you look at the z*table, you see that the number you need for z* for a 95% confidence interval is 1.96. However, when you look up 1.96 on the Ztable, you get a probability of 0.975. Why?
In a nutshell, the Ztable shows only the probability below a certain zvalue, and you want the probability between two zvalues, –z and z. If 95% of the values must lie between –z and z, you expand this idea to notice that a combined 5% of the values lie above z and below –z. So 2.5% of the values lie above z, and 2.5% of the values lie below –z.
To get the total area below this zvalue, take the 95% between –z and z plus the 2.5% below –z, and you get 97.5%. That’s the zvalue with 97.5% area below it. It’s also the number with 95% lying between two zvalues, –z and z.
To avoid all these extra steps and headaches, the z*table has already done this conversion for you. So when you look up 1.96, you automatically find 95% (not 97.5%).

What is the z*value for a 99% confidence level?
Answer: 2.58
The z*table shows the answer: A 99% confidence level has a z*value of 2.58.

What is the z*value for a confidence level of 80%?
Answer: 1.28
The z*table shows the answer: An 80% confidence level has a z*value of 1.28.
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